Question

Suppose that you want to perform a hypothesis test to compare four population means, using independent samples. In each case, decide whether you would

Significance tests
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asked 2021-06-28
Suppose that you want to perform a hypothesis test to compare four population means, using independent samples. In each case, decide whether you would use the one-way ANOVA test, the Kruskal-Wallis test, or neither of these tests. Preliminary data analyses of the samples suggest that the four distributions of the variable a. are not normal but have the same shape. b. are normal and have the same shape.

Expert Answers (1)

2021-06-29
(a) The one-way ANOVA test requires that the data originate from normal populations. Since the population distributions appear to be not normal in this case, it is not appropriate to use the one-way ANOVA test.
The Kruskal-Wallis test requires that the data originate from populations with the same shape distributions. In this case, the distributions appear to have the sameshape and thus it is appropriate to use the Kruskal-Wallis test.
Since it is only appropriate to use the Kruskal-Wallis test, we should use the Kruskal-Wallis test.
(b) The one-way ANOVA test requires that the data originate from normal populations. Since the population distributions appear to be normal in this case, it is appropriate to use the one-way ANOVA test.
The Kruskal-Wallis test requires that the data originate from populations with the same shape distributions. In this case, the distributions appear to have the sameshape and thus it is appropriate to use the Kruskal-Wallis test.
When it is appropriate to use both the one-way ANOVA test and the Kruskal-Wallis test, then it is preferable to use the one-way ANOVA test as the one-way ANOVA test is more powerful than the Kruskal-Wallis test.
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